# math

posted by .

the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now?

the equation for the exponential equation is: A=ao e ^ -kt

ao is the original amount

a is what the population will be

t is the amount of time

k is the rate of growth

• math -

I don't see why the exponent is negative since this an exponentional growth, the negative usually indicates decay.

Anyway...
I would use A = a (e^kt), where t is months
using << the population doubled in size over an 18 month period >>
2 = 1(e^18k)
ln 2 = 18k
k = ln 2/18

so A = 1000 (e^(24*ln2/18))
= 1000(2.51984)
= 2520

another way would be to use

A = 1000(2)t/k and put in t=24
A = 1000(2^1.3333333)
= 2520

## Similar Questions

the population of a town is decreasing at a rate of 1.8% per year. The current population of the own in 12000. a)write and equation that models the population of the town b)how long will it take for the population to decline to one …
2. ### CACULUS- EXPONENTIAL GROWTH

A population of animals in an ecological niche is growing in time so that it's rate of growth dp/dt is related to its current size by the differential equation dp/dt = 900/p^2. If time is measured in years and initially there are P(0) …
3. ### Algebra

Solve. The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how …
4. ### Population growth

The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P = Aekt where A and k are constants. (a) With the aid of appropriate …
5. ### Maths B question - population

The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P = Aekt where A and k are constants. (a) With the aid of appropriate …
6. ### Maths B - Population Growth

The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P=¡¼Ae¡½^kt where A and k are constants. With the aid of appropriate …
7. ### Math

The population of a southern city follows the exponential law. If the population doubled in size over 13 months and the current population is 30,000 what will the population be in 5 years from now?
8. ### Math/Precal

The size of a decreasing population is given by p(t)=P0(2)^-t/7 where p(t) represents the population as time, t, in years and p0 is the initial population what percent of the original population will be there after 10 years?
9. ### Math

The size of a decreasing population is given by p(t)=P0(2)^-t/7 where p(t) represents the population as time, t, in years and p0 is the initial population what percent of the original population will be there after 10 years?
10. ### RTC

The population of a southern city follows the exponential law. If the population doubled in size over 2929 months and the current population is 30 comma 00030,000​, what will the population be 33 years from​ now

More Similar Questions